Current Research

Algebraic and Number Theoretic Methods in Cryptography

Computation and Algorithms in Finite Fields

Elliptic and Hyperelliptic curve cryptography

Research Projects

Elliptic Curve Cryptography

The use of elliptic curves in Public Key Cryptography has been first suggested in 1985. From this date, elliptic curves have
become increasingly popular mainly because the only algorithms that we know to solve the hard problem on which cryptography is
based, namely the elliptic curve discrete logarithm problem, are of exponential complexity. This is in contrast with the existence
of sub-exponential algorithms to solve the factorisation problem on which RSA is based. As a consequence, much shorter keys can be
used in elliptic curve cryptography (ECC) to achieve the same level of security provided by RSA. For instance, a key of 160 bits
in ECC is believed to be as secure as a 1024-bit RSA key.
The goal of this project is to research new fast and secure ways to perform arithmetic on elliptic curves and to implement a
cryptosystem based on these curves.

Even moments of generalized Rudin-Shapiro polynomials, Math. Comp. 74 no. 252, 1923-1935, (2005).
A gp program to precisely compute the moments
of the Rudin-Shapiro polynomial of order q even less than or equal to 32 and the moments of some generalized
Rudin-Shapiro polynomials is available here [moments.gp]
as well as the tables of minimal polynomials for the recurrences
and the first moments [data.gz] and
[data32.gz]